Q: What are the factor combinations of the number 7,221,409?

 A:
Positive:   1 x 722140913 x 55549347 x 15364753 x 136253223 x 32383611 x 11819689 x 104812491 x 2899
Negative: -1 x -7221409-13 x -555493-47 x -153647-53 x -136253-223 x -32383-611 x -11819-689 x -10481-2491 x -2899


How do I find the factor combinations of the number 7,221,409?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 7,221,409, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 7,221,409
-1 -7,221,409

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 7,221,409.

Example:
1 x 7,221,409 = 7,221,409
and
-1 x -7,221,409 = 7,221,409
Notice both answers equal 7,221,409

With that explanation out of the way, let's continue. Next, we take the number 7,221,409 and divide it by 2:

7,221,409 ÷ 2 = 3,610,704.5

If the quotient is a whole number, then 2 and 3,610,704.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 7,221,409
-1 -7,221,409

Now, we try dividing 7,221,409 by 3:

7,221,409 ÷ 3 = 2,407,136.3333

If the quotient is a whole number, then 3 and 2,407,136.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 7,221,409
-1 -7,221,409

Let's try dividing by 4:

7,221,409 ÷ 4 = 1,805,352.25

If the quotient is a whole number, then 4 and 1,805,352.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 7,221,409
-1 7,221,409
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

11347532236116892,4912,89910,48111,81932,383136,253153,647555,4937,221,409
-1-13-47-53-223-611-689-2,491-2,899-10,481-11,819-32,383-136,253-153,647-555,493-7,221,409

More Examples

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